Minimal Construct: Efficient Shortest Path Finding for Mobile Robots in Polygonal Maps

With the advent of polygonal maps finding their way into the navigational software of mobile robots, the Visibility Graph can be used to search for the shortest collision-free path. The nature of the Visibility Graph-based shortest path algorithms is such that first the entire graph is computed in a relatively time-consuming manner. Then, the graph can be searched efficiently any number of times for varying start and target state combinations with the A* or the Dijkstra algorithm. However, real-world environments are typically too dynamic for a map to remain valid for a long time. With the goal of obtaining the shortest path quickly in an ever changing environment, we introduce a rapid path finding algorithm-Minimal Construct-that discovers only a necessary portion of the Visibility Graph around the obstacles that actually get in the way. Collision tests are computed only for lines that seem heuristically promising. This way, shortest paths can be found much faster than with a state-of-the-art Visibility Graph algorithm and as our experiments show, even grid-based A* searches are outperformed in most cases with the added benefit of smoother and shorter paths.